Classification of Einstein metrics on the product of an interval with a three-sphere
Differential Geometry
2011-11-10 v1
Abstract
We present a complete classification of Einstein metrics on the space M = I \times S^3, where I is the interval (0,l) or (0,\infty) or their closures, and we consider separate metric functions f and h (functions of I) for the base and fiber of the Hopf fibration S^1 -> S^3 -> S^2. All such metrics yielding smooth and complete manifolds are included and discussed. The results are surprisingly rich, including many well-known examples and several one-parameter families of metrics with a variety of geometries.
Cite
@article{arxiv.1111.2153,
title = {Classification of Einstein metrics on the product of an interval with a three-sphere},
author = {Curtis T. Asplund and Brian Krummel and Evan Merrell and Robert Rachal and DaGang Yang},
journal= {arXiv preprint arXiv:1111.2153},
year = {2011}
}
Comments
12 pages, no figures. Paper written in 2004